awyers for alleged victims of clergy sexual abuse met with a mediator and a lawyer for the Archdiocese of Boston in Brockton yesterday to discuss their counterproposal to Archbishop Sean P. O'Malley's initial $55 million settlement offer that would pay off 542 outstanding claims against the archdiocese.

Lawyers involved in the case would not disclose the amount they are seeking, but said that the two sides had a frank discussion about the counterproposal, the broad terms of which had already been given last week to Thomas H. Hannigan Jr., the attorney representing the archdiocese.

The lawyers met at the Brockton offices of mediator Paul A. Finn, who presented Hannigan with a detailed written version of the proposal created by a six-lawyer steering committee representing the 47 attorneys whose clients are pressing sexual abuse claims against the archdiocese.

Jeffrey Newman, a steering committee member and lawyer for the Boston firm Greenberg Traurig, which represents more than 260 people with claims against the archdiocese, said the committee did its homework -- often working late into the night -- before the meeting.

''We attempted to create a fair counteroffer that would allow the archdiocese to bring resolution to this situation quickly,'' Newman said. ''We analyzed all the claims and came together as a steering committee on both monetary and nonmonetary terms, and we labored to make sure we communicated it clearly.

''We are all hopeful that Archbishop O'Malley will bring closure to this case soon,'' Newman said.

Another member of the steering committee, Boston attorney Alan L. Cantor, said the proposal was ''fairly developed, fairly precise, and contained some new ideas that we asked the church to think about.''

''We are hoping to hear something back sometime later this week,'' said Cantor, who represents seven people with claims against the archdiocese. ''I really feel that everyone is sincerely trying to get this done. As with any mediation process, there was a fair amount of time spent with people explaining their position and explaining how the other guy's position wasn't going to work, but people are trying to be optimistic.''

While the lawyers wouldn't disclose the terms of their counterproposal yesterday, in the past they have called O'Malley's $55 million offer everything from ''a good start'' to ''woefully inadequate.'' Lawyers for alleged victims also said they would be pursuing nonmonetary issues in the settlement talks, such as discussing ways the Church could prevent future abuse.

The two sides met in a conference room at Commonwealth Mediation and Conciliation, Finn's firm. Hannigan, who has declined to talk publicly about the settlement negotiations since he was named as the archdiocese's chief lawyer by O'Malley earlier this month, did not return calls made to his office yesterday.

The Rev. Christopher Coyne, the spokesman for the archdiocese, wouldn't comment.

O'Malley offered the $55 million earlier this month in a bid to end the massive civil litigation surrounding the worst scandal in the history of the Roman Catholic Church in the United States. The amount appears to be nearly twice what any diocese or archdiocese has paid at one time to settle claims of sexual abuse by clergy or other church employees.

Because the money would be divided among so many plaintiffs, lawyers for alleged victims almost immediately said they considered the offer a starting point for negotiations, rather than an end to the legal challenge. Even so, they said that O'Malley's offer, made less than two weeks after his installation as archbishop, was in sharp contrast to more than a year of frustrating and unproductive settlement talks that preceded it.

Lawyers said O'Malley's gesture was so positive that they agreed to suspend almost all active litigation in the 542 claims. Under the O'Malley proposal, the archdiocese would waive its legal defenses but would not participate in dividing up the money.